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BOUNDS ON PRICES FOR ASIAN OPTIONS VIA FOURIER METHODS

Part of: Mathematical finance Harmonic analysis in several variables Stochastic processes

Published online by Cambridge University Press:  19 February 2016

SCOTT ALEXANDER Open the ORCID record for SCOTT ALEXANDER [Opens in a new window] ,
ALEXANDER NOVIKOV  and
NINO KORDZAKHIA
SCOTT ALEXANDER*
Affiliation:
University of Technology, Sydney, NSW, Australia email [email protected], [email protected]
ALEXANDER NOVIKOV
Affiliation:
University of Technology, Sydney, NSW, Australia email [email protected], [email protected]
NINO KORDZAKHIA
Affiliation:
Macquarie University, Sydney, NSW, Australia email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

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The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric Lévy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.

Keywords

Asian optionlower boundcharacteristic functionFourier transforminverse Fourier transformexponential damping

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 91G20: Derivative securities 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 299 - 318
Copyright
© 2016 Australian Mathematical Society 

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